Methodology

To calculate \(E_{ij}\), we considered the diffusion of theoretical particles in an ecosystem. These particles are the resultant of an activity, such as contaminants or sediment, and they difuse from the source of the activity. Three types of particles have been considered, in order to model a certain sinking rate. Their combination will allow to represent each activity by a unique signature.

• slow-sinking particles (previously < 4 µm): e.g. clay, dissolved organic matter, small bacteria, viruses, chemical components, proteins
• medium-sinking particles (previously between 4 µm and 2 mm): e.g. sand, silt, small particulate organic matter, large bacteria, phytoplankton, zooplankton
• fast-sinking particles (previously > 2 mm): e.g. gravel, large particulate organic matter, clusters of dead organisms, large zooplankton, larger organisms

We simulated the dispersion of these particles using the distance from the source and an inverse logarithm relationship, to account for a ‘journey’ in a 2D environment while reducing the contribution of highest values. A cutoff distance for each particle type was used to simulate sedimentation, thus establishing a threshold after which the exposure becomes negligible.

The general equation for \(E_{ij}\) is:

\[ \left\{\begin{matrix} E_{ij} = \frac{1}{ln(D_{ij} + 1)} & D_{ij} < T \\ E_{ij} = 0 & D_{ij} > T \end{matrix}\right. \]

• \(D_{ij}\) is the minimal distance from the source of activity
• \(T\) is the threshold defined by the cutoff distances of each particle type
• \(i\) is a station
• \(j\) is a human activity

Cutoff distance for \(T\) (in meters) has been initialized as such:

⚠️ These values need to be groundtruthed by litterature research and expert opinion.

\(D_{ij}\) has been calculated with least-cost pathfinding methods from the package gdistance. To compute the trajectory of the particles of each class, we established a connectivity model based on a ‘resistance seascape’ concept. First, we created a raster considering our study area, whose cell can be selected to obtain the path connecting start (source of the activity) and end (raster cell) points. Each cell has a cost to be included in this path, which is defined on physical constraints to account for environmental behaviour. The length of the final path then gives the minimal distance.

We considered three underlying principles for the physical constraints:

• marine ecosystems: particles cannot disperse on land
• gravity: particles disperse easily from shallow to deeper depths, while the reverse is difficult
• hydrodynamism: particles disperse according to local hydrodynamical currents

Thus, the connectivity model considered: (i) coasts and islands as boundaries unselectable by the algorithm, (ii) bathymetry, (iii) river plumes as hydrodynamical fronts with an intensity and a direction (a complete circulation model in BSI is not yet available).

⚠️ For now, only the two first constraints are implemented.

These constraints are included the transition function \(f_{j}\), used by costDistance() when creating the least-cost path. It computes connectivity values from a cell to its eight closest neighbours (chess queen configuration), with these conditions:

• land is set with a connectivity of 0, so that corresponding cells cannot be chosen by the pathfinding algorithm
• bathymetry is compared between two cells:
  • when point A is shallower than point B, connectivity is high
  • when point A is deeper than point B, connectivity is low (with a certain diffusion)
• CDOM content (proxy of hydrodynamism) is compared between two cells (NOT IMPLEMENTED YET)

Values of the parameters used for bathymetry and hydrodynamism contraints depend on the types of particle:

• slow-sinking particles: influenced primarily by hydrodynamics and diffusing over extended areas; gravity eventually sinks them; easily resuspended
• medium-sinking particles: particles both sinking due to gravity and spreading by hydrodynamic influence, resuspension possible but difficult
• fast-sinking particles: dense aggregates that sink easily due to gravity and are unaffected by hydrodynamical effects; resuspension is highly difficult

The equation for \(D_{ij}\) is then:

\[ D_{ij} = \sum_{k}^{s,m,f} f_{k} \left( B_{i}, H_{i}, T_{k} \right) . p_{jk} \]

• \(f_{k}\) is the transition function
• \(B_{i}\) is the bathymetry constraint
• \(H_{i}\) is the hydrodynamics constraint
• \(T_{k}\) is the cutoff distance
• \(p_{jk}\) is the proportion of each type of particle
• \(i\) is a station
• \(j\) is a human activity
• \(k\) is the particle type (slow, medium, fast sinking)

With the transition functions \(f_{j}\):

And the proportion of each particule size \(p_{jk}\):

⚠️ These values need to be groundtruthed by litterature research and expert opinion.

The combination of each particule size uses a weighted addition, but different relationships may be tested in the future. Finally, \(E_{ij}\) have been standardized by the minimal and maximal values to allow comparisons.

Methodology

We extracted data from a global database for the St. Lawrence, for all fishing events occuring within the Baie des Sept-Îles. Four types of gears (traps, bottom-trawls, nets and dredges) have been considered in the bay between 2010 and 2015. Eight species have been gathered (see table at the top of this page).

As each gear was not used consistently during this period, we averaged the number of fishing events to obtain a proxy of fishing intensity. Furthermore, we modified this proxy with a smoothing function in order to ‘diffuse’ the signal around the actual event.